Problem: Solve for $x$ and $y$ using elimination. ${6x+y = 27}$ ${-5x-y = -23}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {6x+y = 27}\thinspace$ to find $y$ ${6}{(4)}{ + y = 27}$ $24+y = 27$ $24{-24} + y = 27{-24}$ ${y = 3}$ You can also plug ${x = 4}$ into $\thinspace {-5x-y = -23}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - y = -23}$ ${y = 3}$